Question 2 (cont.): Make a scatter plot of the filtered dataset based on CO2 emssions and gdpPercap

ScatterPlot <- GapminderFilteredYear %>%
  ggplot(., aes(
    x = gdpPercap,
    y = `CO2 emissions (metric tons per capita)`
  )) +
  geom_point() +
  theme_classic()

## Warning: Removed 151 rows containing missing values (geom_point).

From our dataset, we can see that there is a positively linear relationship between CO2 emissions and GDP per capita. Now lets investigate further on how strong the correlation is based on the pearson correlation (R) coefficient.

Question 3: On the filtered data, calculate the pearson correlation of ‘CO2 emissions (metric tons per capita)’ and gdpPercap. What is the Pearson R value and associated p value?

test <- "pearson"
rm_na <- "complete.obs"
pearson_corr <- cor(GapminderFilteredYear$`CO2 emissions (metric tons per capita)`,
  GapminderFilteredYear$gdpPercap,
  method = test,
  use = rm_na
) * 100

## `geom_smooth()` using formula 'y ~ x'

## Warning: Removed 151 rows containing non-finite values (stat_smooth).

## Warning: Removed 151 rows containing non-finite values (stat_cor).

## Warning: Removed 151 rows containing missing values (geom_point).

## The pearson correlation coefficient between CO2 emissions and GDP per capita is 92.6%

From what we can see here, the pearson correlation coefficient is approximately 92.61%, meaning that there is a strong positive correlation between CO2 emissions and GDP per capita in all countries in the year of 1962. In addition, the p-value (2.2 * 10^-6) is less than 0.05, meaning that the correlation of the two variables are significant to one another. Now lets take a look at all years and see which has the highest pearson correlation coefficient.

Question 4: On the unfiltered data, answer “In what year is the correlation between ‘CO2 emissions (metric tons per capita)’ and gdpPercap the strongest?” Filter the dataset to that year for the next step…

test <- "pearson"
rm_na <- "complete.obs"
CO2_year <- vector(mode = "list")
gdpPercap_year <- vector(mode = "list")
PearsonCorrYears <- vector(mode = "list")
YearChartoNum <- vector(mode = "list")



GapminderYear <- GapminderData %>% # selecting the all the unique years iteration
  select(Year) %>%
  unique() %>%
  pull() %>%
  as.character() # For names in the list

PearsonCorrYears <- GapminderYear %>% # Make into a list by iterating through the years
  sapply(.,
    USE.NAMES = TRUE,
    simplify = FALSE,
    function(year) {
      YearChartoNum[[year]] <- year %>% # Convert characters to numeric values
        as.numeric()

      CO2_year[[year]] <- GapminderData %>% # list for the CO2 emissions by year
        filter(Year == YearChartoNum[[year]]) %>%
        select(`CO2 emissions (metric tons per capita)`) %>%
        pull()

      gdpPercap_year[[year]] <- GapminderData %>% # list for the GDP per capita by
        filter(Year == YearChartoNum[[year]]) %>% # year
        select(gdpPercap) %>%
        pull()

      cor(
        x = GapminderData %>% # Pearson Correlation coefficient iterated by year
          filter(Year == YearChartoNum[[year]]) %>%
          select(`CO2 emissions (metric tons per capita)`) %>%
          pull(),
        y = gdpPercap_year[[year]],
        method = test,
        use = rm_na
      )
    }
  ) %>% unlist()

After iterating over the years in the Gapminder dataset, we can see that the highest Pearson correlation coefficient occurs in 1967 suggesting that year has the strongest correlation (93.88%) between CO2 emissions and GDP per capita. Now lets filter the Gapminder dataset again with that year and plot a scatterplot through plotly.

Question 5: Using plotly, create an interactive scatter plot comparing ‘CO2 emissions (metric tons per capita)’ and gdpPercap, where the point size is determined by pop (population) and the color is determined by the continent. You can easily convert any ggplot plot to a plotly plot using the ggplotly() command.

PearsonCorrMaxYear <- PearsonCorrYears[which.max(PearsonCorrYears)] %>%
  names() %>%
  as.numeric() # Finding the max year for the analysis

GapminderFilteredMax <- GapminderData %>% ## Filter by year with the highest Pearson
  filter(Year == PearsonCorrMaxYear) ## correlation coefficient of CO2 and GDP

GapminderMaxplot <- GapminderFilteredMax %>% ## ggplot implementation
  ggplot(., aes(
    x = `CO2 emissions (metric tons per capita)`,
    y = gdpPercap,
    size = pop
  )) +
  geom_point() +
  theme_classic()

Here is the plotly implementation of the Gapminder dataset during the year of 1962. The scatterplot is interactive and you can see the different values (gdpPercap, CO2 emissions) in each point of the plot.

New Question 1: What is the relationship between continent and ‘Energy use (kg of oil equivalent per capita)’? (stats test needed)

GapminderContinentEnergyUse <- GapminderData %>%
  select(continent, `Energy use (kg of oil equivalent per capita)`) %>%
  na.omit()

In order to determine the exact relationship between the each continent (categorical variable) and Energy use (kg of oil equivalent per capita) (continuous variable), we need to construct a linear model of the data and do ANOVA across all the continent groups.

lm(
  formula = `Energy use (kg of oil equivalent per capita)` ~ continent,
  data = GapminderContinentEnergyUse
) %>% summary()

## 
## Call:
## lm(formula = `Energy use (kg of oil equivalent per capita)` ~ 
##     continent, data = GapminderContinentEnergyUse)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2796.0 -1107.5  -349.1   276.8 12904.4 
## 
## Coefficients:
##                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          698.5      137.2   5.090 4.42e-07 ***
## continentAmericas   1005.1      196.9   5.105 4.10e-07 ***
## continentAsia       1168.8      197.7   5.911 4.93e-09 ***
## continentEurope     2447.5      183.0  13.377  < 2e-16 ***
## continentOceania    3281.8      454.1   7.227 1.11e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1936 on 843 degrees of freedom
## Multiple R-squared:  0.1963, Adjusted R-squared:  0.1924 
## F-statistic: 51.46 on 4 and 843 DF,  p-value: < 2.2e-16

From the results above, we have the following equation:

Y = continentAmericas * x1 + continentAsia * x2 + continentEurope * x3 + continentOceania * x4 + Intercept

Definitions of the variables:
Y = Energy use (kg of oil equivalent per capita) (continuous variable)
x1 = North and South America (categrorical variable i.e 0 or 1)
x2 = Asia (categrorical variable i.e 0 or 1)
x3 = Europe (categrorical variable i.e 0 or 1)
x4 = Oceania (categrorical variable i.e 0 or 1)
continentAmericas = 1005.1
continentAsia = 1168.8
continentEurope = 2447.5
continentOceania = 3281.8
Intercept = 698.5

We can conclude that since all the p-values are less than 0.05 for each continent, we can reject the null hypothesis and interpret that all the continent variables have a statistically significant relationship. Furthermore, since all the continent coefficents are positive, we can see that each continent has a positive relationship with the Energy use (kg of oil equivalent per capita).

New Question 2: Is there a significant difference between Europe and Asia with respect to ‘Imports of goods and services (% of GDP)’ in the years after 1990? (stats test needed)

continents_of_interest <- c("Europe", "Asia")
variables_of_interest <- c("continent", "Year", "Imports of goods and services (% of GDP)")

Euro_Asia_Imports <- GapminderData %>%
  dplyr::filter(continent %in% continents_of_interest &
    Year > 1990) %>%
  dplyr::select(variables_of_interest) %>%
  na.omit()

## Note: Using an external vector in selections is ambiguous.
## ℹ Use `all_of(variables_of_interest)` instead of `variables_of_interest` to silence this message.
## ℹ See <https://tidyselect.r-lib.org/reference/faq-external-vector.html>.
## This message is displayed once per session.

ggboxplot(Euro_Asia_Imports,
  x = "continent",
  y = "Imports of goods and services (% of GDP)",
  color = "continent",
  add = "jitter",
  shape = "continent"
)

In order to determine whether or not there is a significant difference between Europe and Asia based on Imports of goods and services (% of GDP) after 1990, we need to determine whether we use the t-test or the Welch t-test.

From what we see from this boxplot above, there are differences of variation (i.e. spread) of the data between Asia and Europe, so the Welch t-test is the most appropriate for this type of test.

t.test(`Imports of goods and services (% of GDP)` ~ continent,
  data = Euro_Asia_Imports
)

## 
##  Welch Two Sample t-test
## 
## data:  Imports of goods and services (% of GDP) by continent
## t = 1.3552, df = 137.53, p-value = 0.1776
## alternative hypothesis: true difference in means between group Asia and group Europe is not equal to 0
## 95 percent confidence interval:
##  -2.321099 12.433240
## sample estimates:
##   mean in group Asia mean in group Europe 
##             46.84531             41.78924

Since the p-value (0.1776) > 0.05, we need to fail to reject the null hypothesis. We can conclude that there is not a statistically significant difference between Europe and Asia with respect to ‘Imports of goods and services (% of GDP)’ in the years after 1990.

New Question 3: What is the country (or countries) that has the highest ‘Population density (people per sq. km of land area)’ across all years? (i.e., which country has the highest average ranking in this category across each time point in the dataset?)

order_of_variables <- c(
  "Year",
  "Country Name",
  "Population density (people per sq. km of land area)"
)

GapminderPopDensity <- GapminderData %>%
  select(
    `Country Name`,
    `Population density (people per sq. km of land area)`,
    Year
  ) %>%
  na.omit() %>%
  dplyr::group_by(Year) %>%
  slice(which.max(`Population density (people per sq. km of land area)`)) %>%
  dplyr::select(order_of_variables)

## Note: Using an external vector in selections is ambiguous.
## ℹ Use `all_of(order_of_variables)` instead of `order_of_variables` to silence this message.
## ℹ See <https://tidyselect.r-lib.org/reference/faq-external-vector.html>.
## This message is displayed once per session.

The datatable below shows which country has the highest average population density in each time point in the dataset. From what we see, Monaco and Macao SAR, China have been dominating the population density from 1962-2007.

R for DataScience

Justin Guerra

11/12/2021

Question 1: Reading in the Gapminder Data into R

Question 2: Filter Gapminder dataset by year of 1962 and make a scatter plot